The symbolic defect of an ideal |
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Authors: | Federico Galetto Anthony V Geramita Yong-Su Shin Adam Van Tuyl |
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Institution: | 1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4L8, United States of America;2. Department of Mathematics, Sungshin Women''s University, Seoul, 136-742, Republic of Korea |
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Abstract: | Let I be a homogeneous ideal of . To compare , the m-th symbolic power of I, with , the regular m-th power, we introduce the m-th symbolic defect of I, denoted . Precisely, is the minimal number of generators of the R-module , or equivalently, the minimal number of generators one must add to to make . In this paper, we take the first step towards understanding the symbolic defect by considering the case that I is either the defining ideal of a star configuration or the ideal associated to a finite set of points in . We are specifically interested in identifying ideals I with . |
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Keywords: | 13A15 14M05 Symbolic powers Regular powers Points Star configurations |
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